Sun publisher News International, Telegraph Media Group, Associated Newspapers – which owns the Daily Mail – Trinity Mirror and Express Newspapers have drawn up a draft alternative royal charter, which will be put to the privy council later on Thursday.

Hacked Off, which has been campaigning for press victims, immediately condemned the move.

In a strongly worded statement, associate director Evan Harris branded the development as a "temper tantrum by some powerful people used to having their own way".

He added: "The royal charter agreed by parliament is not going to be reopened at the request of Mr Murdoch, Mr Desmond and Mr Dacre," a reference to Rupert Murdoch, owner the Sun and the Times, Richard Desmond, owner of the Express and Daily Star, and Paul Dacre, editor of the Daily Mail.

All four industry bodies, including the Newspaper Society, which represents national and local titles, are backing the plan which is closely based on the draft charter the industry agreed with the government on 12 February.

The Newspaper Society said the plans were "a workable, practical way swiftly to deliver the Leveson recommendations, which the industry accepts, without any form of state-sponsored regulation that would endanger freedom of speech".

"It is a simple idea. The whole purpose of it is to remove the logjam," said a source.

The Guardian and the Financial Times were not privy to the details discussions ahead of Thursday's announcement and have not signed up to the deal.

Peter Wright, the Associated Newspapers executive tasked with dealing with Leveson negotiations, told BBC Radio 4's World at One he had spoken to the editors of the Guardian and the FT and they both thought it was "a good idea to get the ball rolling" but conceded that no editor "has signed up on the specifics".

A spokesman for the Mirror said: "We are supporting this industry-wide proposal."

Chris Blackhurst, the editor of the Independent, said he did not object to the move for a rival royal charter but lack of independence from the newspaper industry could be a stumbling block.

"I have always taken the view that in the end, ever since Leveson was appointed, the politicians would decide on press regulation. We have to come up with a system that is acceptable to them. Leveson used the phrase 'independent self-regulation'. That word 'independent' is crucial. If it's not independent, it won't be acceptable."

Les Hinton, the former chief executive of News International, tweeted: "No small thing to go against will of parliament. Shows depth of feeling among newspaper groups which are usually bitter rivals."

The government, which was taken by surprise by the newspaper industry's move, said it had already done a deal with Labour and the Liberal Democrats.

A spokesman for culture secretary Maria Miller said: "The Privy Council Office will need to look at this proposal. We have already set out a draft royal charter which has cross-party agreement."

He added: "We want to see a tough independent self-regulator implemented swiftly. The royal charter published on the 18 March followed 21 weeks of discussion and has cross-party agreement."

But the culture select committee chairman John Whittingdale came in behind the newspaper industry, saying their version of the latest royal charter met all the Leveson principles. His committee is conducting an inquiry into the all-party talks that led to the completed all-party-endorsed version of the royal charter.

Harriet Harman, Labour's deputy leader and the shadow culture, media and sport secretary said: "The royal charter implements Lord Justice Leveson's recommendations. It was supported unanimously by the House of Commons and had the full backing of the House of Lords. The important thing is that we get on with implementation."

Significantly, the newspapers' royal charter does not include the government proposal, championed by Cameron's policy tsar Oliver Letwin, that the charter could only be dissolved with a two-thirds majority vote of both houses of parliament.

Under the proposals the government's right to dissolve the royal charter in the case of another systemic breach of self-regulation, such as phone hacking, would be replaced by a "triple lock" system centring on the industry.

The charter could only be amended or withdrawn with the unanimous permission of the independent recognition panel that the government is planning to set up to audit the new press regulator's performance every three years.

In addition, it would also need the unanimous permission of the board of the new regulator and finally the unanimous agreement of four industry bodies: the Newspaper Society, the Newspaper Publishers Association, the Periodical Publishers' Association and the Scottish Newspaper Society. "This is a very high bar," said a source from one of the newspaper groups.

Publishers have threatened to boycott the government's plans following an early-morning deal between the three main parties and press group Hacked Off on 18 March, arguing a royal charter backed by statute would end 300 years of press freedom.

The Guardian has reservations about the government's plans for the royal charter, with editor-in-chief Alan Rusbridger urging Cameron to delay it for a year to give the industry a chance to set up a regulator based on Westminster plans and prove it could get its house in order without a charter.

After a month of scrutiny, the newspaper industry received legal advice suggesting it has the right to apply for its own royal charter just like any other profession. Many professions have done so in the past, including accountants and surveyors.

The independence of the new regulatory authority, however, could be questioned after it emerged that the industry wants to hold a veto on all appointments to the board. They have argued that this is to ensure regional newspapers, which provide 40% of the funding, aren't squeezed out of the picture by independent members who may not be familiar enough with the workings of the industry.

This will be seen as a major weakness in the bid to launch a rival press regulator as it could lead to accusations that News International and Associated Newspapers still want to control the board. Their influence over appointments at the discredited Press Complaints Commission was seen as the Achilles' heel of the existing regulatory body, which led to poor decisions being made and eventually to its implosion after 21 years as a result of its failure to get to grips with the News of the World phone-hacking scandal.

Media commentator Steve Hewlett said the "other side will smell a rat" over the appointments process. "This will be portrayed no doubt as marking your own homework," he said. '

Sources said the veto or guarantee would not be contained in a statute but in the articles of association of the new regulator, which could still be negotiated to ensure all national and regional newspapers come on board.

There will also be controversy over the newspapers' plans to ditch the government-backed proposal for a whistleblowers' hotline.

Harris said: "A section of the industry is to trying to reopen a battle that is over, and which they have lost. It is entirely predictable, but what they are doing is putting up two fingers to political leaders, parliament, the judge, the victims and, according to polls, most of their readers. Their position is untenable. We live in a parliamentary democracy and abide by the rule of law. They are behaving like children that have not got their way and now thrown everything out of the pram.

"I cannot imagine how David Cameron could possibly go back on what he said agreed. Parts of the industry can stay out out of the system of regulation. There is a system of incentives in place to join the system of regulation, and it is for the industry to stay outside of it if it so wishes."

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